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                                <h1 id="&#x7B2C;&#x4E03;&#x7AE0;-tensorflow&#x5E94;&#x7528;">&#x7B2C;&#x4E03;&#x7AE0; Tensorflow&#x5E94;&#x7528;</h1>
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<p>&#x91C7;&#x7528;&#x4E24;&#x6B21;&#x6D4B;&#x8BD5;&#x76F8;&#x51CF;&#x7684;&#x65B9;&#x6CD5;&#x6765;&#x907F;&#x514D;&#x8F6C;&#x5B50;&#x5E95;&#x90E8;&#x53CA;&#x9876;&#x90E8;&#x6DF7;&#x51DD;&#x571F;&#x5BF9;&#x626D;&#x77E9;&#x7684;&#x5F71;&#x54CD;&#x3002;&#x5206;&#x522B;&#x5728;&#x5341;&#x5B57;&#x67B6;&#x79BB;&#x5E95;&#x90E8;&#x7EA6;50mm&#x548C;150mm&#x65F6;&#x6D4B;&#x8BD5;<code>T-N</code>&#x66F2;&#x7EBF;&#xFF0C;&#x6709;&#x6548;&#x6D4B;&#x8BD5;&#x8F6C;&#x5B50;&#x9AD8;&#x5EA6;&#x4E3A;100mm&#xFF0C;&#x5728;&#x6D4B;&#x8BD5;&#x524D;&#x91C7;&#x7528;0.65rps&#x7684;&#x901F;&#x5EA6;&#x9884;&#x526A;&#x5207;&#x6DF7;&#x51DD;&#x571F;10s&#xFF0C;&#x7136;&#x540E;&#x91C7;&#x7528;&#x5982;&#x56FE;&#x6240;&#x793A;&#x7684;&#x9636;&#x68AF;&#x9012;&#x51CF;&#x7684;&#x65B9;&#x5F0F;&#x8FDB;&#x884C;&#x6D4B;&#x8BD5;&#xFF0C;&#x8F6C;&#x901F;&#x4E3A;0.60&#x3001;0.55&#x3001;0.5&#x3001;0.45&#x3001;0.4&#x3001;0.35&#x3001;0.3&#x3001;0.25&#x3001;0.2&#x3001;0.15rps&#x5341;&#x4E2A;&#x9012;&#x51CF;&#x9636;&#x68AF;&#x5F0F;&#x7684;&#x65B9;&#x5F0F;&#x8FDB;&#x884C;&#x6D4B;&#x8BD5;&#xFF0C;&#x6BCF;&#x4E2A;&#x9636;&#x68AF;&#x6D4B;&#x8BD5;25&#x79D2;&#xFF0C;&#x91C7;&#x96C6;100&#x4E2A;&#x626D;&#x77E9;&#x6570;&#x636E;&#xFF0C;&#x7A0B;&#x5E8F;&#x81EA;&#x52A8;&#x820D;&#x5F03;&#x6570;&#x636E;&#x524D;&#x9762;&#x7684;40&#x4E2A;&#x70B9;&#xFF0C;&#x53D6;&#x540E;&#x9762;&#x7684;60&#x4E2A;&#x70B9;&#x7684;&#x5E73;&#x5747;&#x503C;&#x4F5C;&#x4E3A;&#x8BE5;&#x901F;&#x7387;&#x4E0B;&#x7684;&#x626D;&#x77E9;&#x503C;&#x3002;&#x8BBE;&#x8BA1;&#x7A0B;&#x5E8F;&#x91C7;&#x7528;&#x975E;&#x7EBF;&#x6027;&#x62DF;&#x5408;&#x7684;&#x65B9;&#x5F0F;&#x6765;&#x6C42;&#x5F97;&#x7C98;&#x5EA6;&#x548C;&#x5C48;&#x670D;&#x5E94;&#x529B;&#x3002;</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>&#x3D5;</mi><mrow><mi>m</mi><mi>o</mi><mi>d</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>T</mi><mrow><mn>5</mn><mn>0</mn></mrow></msub><mo>&#x2212;</mo><msub><mi>T</mi><mrow><mn>1</mn><mn>5</mn><mn>0</mn></mrow></msub></mrow><mrow><mn>4</mn><mi>&#x3C0;</mi><mi>h</mi><mi>&#x3BC;</mi></mrow></mfrac><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msubsup><mi>R</mi><mrow><mn>1</mn></mrow><mn>2</mn></msubsup></mrow></mfrac><mo>&#x2212;</mo><mfrac><mrow><mn>2</mn><mi>&#x3C0;</mi><mi>h</mi><msub><mi>&#x3C4;</mi><mn>0</mn></msub></mrow><mrow><msub><mi>T</mi><mrow><mn>5</mn><mn>0</mn></mrow></msub><mo>&#x2212;</mo><msub><mi>T</mi><mrow><mn>1</mn><mn>5</mn><mn>0</mn></mrow></msub></mrow></mfrac><mo>)</mo><mo>&#x2212;</mo><mfrac><mrow><msub><mi>&#x3C4;</mi><mn>0</mn></msub></mrow><mrow><mn>2</mn><mi>&#x3BC;</mi></mrow></mfrac><mi>l</mi><mi>n</mi><mo>(</mo><mfrac><mrow><msub><mi>T</mi><mrow><mn>5</mn><mn>0</mn></mrow></msub><mo>&#x2212;</mo><msub><mi>T</mi><mrow><mn>1</mn><mn>5</mn><mn>0</mn></mrow></msub></mrow><mrow><mn>2</mn><mi>&#x3C0;</mi><mi>h</mi><msub><mi>&#x3C4;</mi><mn>0</mn></msub><msubsup><mi>R</mi><mn>1</mn><mn>2</mn></msubsup></mrow></mfrac><mo>)</mo></mrow><annotation encoding="application/x-tex">\phi_{mod}=\frac{T_{50}-T_{150}}{4\pi h \mu}(\frac{1}{R_{1}^2}-\frac{2\pi h \tau_0}{T_{50}-T_{150}})-\frac{\tau_0}{2\mu}ln(\frac{T_{50}-T_{150}}{2\pi h \tau_0 R_1^2})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.8962079999999999em;"></span><span class="strut bottom" style="height:1.462648em;vertical-align:-0.56644em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">&#x3D5;</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">m</span><span class="mord mathit mtight">o</span><span class="mord mathit mtight">d</span></span></span></span><span 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style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathrm mtight">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mbin">&#x2212;</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.345em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">5</span><span class="mord mathrm mtight">0</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin mtight">&#x2212;</span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">1</span><span class="mord mathrm mtight">5</span><span class="mord mathrm mtight">0</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.4100999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight" style="margin-right:0.03588em;">&#x3C0;</span><span class="mord mathit mtight">h</span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.1132em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mclose">)</span><span class="mbin">&#x2212;</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.345em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">&#x3BC;</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.4100999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.1132em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="mord mathit">n</span><span class="mopen">(</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.37358em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight" style="margin-right:0.03588em;">&#x3C0;</span><span class="mord mathit mtight">h</span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.1132em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist"><span style="top:0.27551428571428577em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span style="top:-0.34480000000000005em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.4100999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">5</span><span class="mord mathrm mtight">0</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin mtight">&#x2212;</span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">1</span><span class="mord mathrm mtight">5</span><span class="mord mathrm mtight">0</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mclose">)</span></span></span></span></p>
<p>&#x5176;&#x4E2D;&#xFF0C;$\phi<em>{mod}$ &#x662F;&#x91C7;&#x7528;&#x5047;&#x8BBE;&#x7684;&#x7C98;&#x5EA6;$\mu$&#x548C;&#x5C48;&#x670D;&#x5E94;&#x529B;$\tau_0$&#x8BA1;&#x7B97;&#x5F97;&#x5230;&#x7684;&#x8F6C;&#x901F;&#xFF0C;$h$&#x662F;0.1m&#xFF0C;$T</em>{150}$&#x662F;&#x8F6C;&#x5B50;&#x79BB;&#x5E95;&#x90E8;150mm&#x65F6;&#x6D4B;&#x5F97;&#x7684;&#x626D;&#x77E9;&#xFF0C;$T_{50}$&#x662F;&#x8F6C;&#x5B50;&#x79BB;&#x5E95;&#x90E8;50mm&#x65F6;&#x6D4B;&#x5F97;&#x7684;&#x626D;&#x77E9;&#xFF0C;$R1$&#x662F;0.1m&#x3002;</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>M</mi><mi>S</mi><mi>E</mi><mo>=</mo><msqrt><mrow><mfrac><mrow><msubsup><mo>&#x2211;</mo><mi>i</mi><mi>n</mi></msubsup><mo>(</mo><msubsup><mi>&#x3D5;</mi><mrow><mi>m</mi><mi>o</mi><mi>d</mi></mrow><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup><mo>&#x2212;</mo><msubsup><mi>&#x3D5;</mi><mrow><mi>m</mi><mi>e</mi><mi>a</mi></mrow><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup><msup><mo>)</mo><mn>2</mn></msup></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow><annotation encoding="application/x-tex">MSE=\sqrt{\frac{\sum_i^n(\phi_{mod}^{(i)}-\phi_{mea}^{(i)})^2}{n}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.4505435em;"></span><span class="strut bottom" style="height:1.84002em;vertical-align:-0.3894765em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">M</span><span class="mord mathit" style="margin-right:0.05764em;">S</span><span class="mord mathit" style="margin-right:0.05764em;">E</span><span class="mrel">=</span><span class="mord sqrt"><span class="sqrt-sign" style="top:-0.26054350000000004em;"><span class="style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing size2">&#x221A;</span></span></span><span class="vlist"><span style="top:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:1em;">&#x200B;</span></span><span class="mord textstyle cramped"><span class="mord reset-textstyle textstyle cramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.345em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">n</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.534707em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mop mtight"><span class="mop op-symbol small-op mtight" style="top:0.074995em;">&#x2211;</span><span class="msupsub"><span class="vlist"><span style="top:0.32101em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span style="top:-0.397em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">n</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mopen mtight">(</span><span class="mord mtight"><span class="mord mathit mtight">&#x3D5;</span><span class="msupsub"><span class="vlist"><span style="top:0.3112285714285714em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mord mathit mtight">m</span><span class="mord mathit mtight">o</span><span class="mord mathit mtight">d</span></span></span></span><span style="top:-0.5233714285714286em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mopen mtight">(</span><span class="mord mathit mtight">i</span><span class="mclose mtight">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin mtight">&#x2212;</span><span class="mord mtight"><span class="mord mathit mtight">&#x3D5;</span><span class="msupsub"><span class="vlist"><span style="top:0.12274285714285718em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mord mathit mtight">m</span><span class="mord mathit mtight">e</span><span class="mord mathit mtight">a</span></span></span></span><span style="top:-0.5233714285714286em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mopen mtight">(</span><span class="mord mathit mtight">i</span><span class="mclose mtight">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose mtight"><span class="mclose mtight">)</span><span class="msupsub"><span class="vlist"><span style="top:-0.286em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span></span></span><span style="top:-1.3705435em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:1em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped sqrt-line"></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:1em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></p>
<p>&#x5176;&#x4E2D;$MSE$&#x662F;&#x5747;&#x65B9;&#x5DEE;&#xFF0C;$\phi_{mea}$&#x4E3A;&#x6D4B;&#x91CF;&#x5F97;&#x5230;&#x7684;&#x8F6C;&#x901F;&#x3002;&#x901A;&#x8FC7;&#x975E;&#x7EBF;&#x6027;&#x62DF;&#x5408;&#xFF0C;&#x5F97;&#x5230;&#x4F7F;$MSE$&#x6700;&#x5C0F;&#x7684;&#x7C98;&#x5EA6;$\mu$&#x548C;&#x5C48;&#x670D;&#x5E94;&#x529B;$\tau_0$&#x3002;</p>
<table>
<thead>
<tr>
<th>$\phi_{mea}$</th>
<th>$T_{150}$</th>
<th>$ T_{50}$</th>
<th>$\Delta T = T<em>{150}-T</em>{50}$</th>
</tr>
</thead>
<tbody>
<tr>
<td>0.6</td>
<td>5.604385</td>
<td>1.205713</td>
<td>4.398672</td>
</tr>
<tr>
<td>0.55</td>
<td>5.006138</td>
<td>1.189483</td>
<td>3.816655</td>
</tr>
<tr>
<td>0.5</td>
<td>4.769772</td>
<td>1.150114</td>
<td>3.619659</td>
</tr>
<tr>
<td>0.45</td>
<td>4.378935</td>
<td>1.149605</td>
<td>3.22933</td>
</tr>
<tr>
<td>0.4</td>
<td>4.041924</td>
<td>1.118228</td>
<td>2.923696</td>
</tr>
<tr>
<td>0.35</td>
<td>3.964252</td>
<td>1.074618</td>
<td>2.889634</td>
</tr>
<tr>
<td>0.3</td>
<td>3.679724</td>
<td>1.00952</td>
<td>2.670203</td>
</tr>
<tr>
<td>0.25</td>
<td>3.459106</td>
<td>0.992959</td>
<td>2.466147</td>
</tr>
<tr>
<td>0.2</td>
<td>3.17693</td>
<td>0.889285</td>
<td>2.287645</td>
</tr>
<tr>
<td>0.15</td>
<td>2.89349</td>
<td>0.881943</td>
<td>2.011547</td>
</tr>
</tbody>
</table>
<p>&#x6839;&#x636E;&#x5DF2;&#x77E5;&#x7684;&#x6570;&#x636E;&#xFF0C;&#x516C;&#x5F0F;&#x7B80;&#x5316;&#x4E3A;</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>&#x3D5;</mi><mrow><mi>m</mi><mi>o</mi><mi>d</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">&#x394;</mi><mi>T</mi></mrow><mrow><mn>4</mn><mi>&#x3C0;</mi><mi>h</mi><mi>&#x3BC;</mi></mrow></mfrac><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msubsup><mi>R</mi><mrow><mn>1</mn></mrow><mn>2</mn></msubsup></mrow></mfrac><mo>&#x2212;</mo><mfrac><mrow><mn>2</mn><mi>&#x3C0;</mi><mi>h</mi><msub><mi>&#x3C4;</mi><mn>0</mn></msub></mrow><mrow><mi mathvariant="normal">&#x394;</mi><mi>T</mi></mrow></mfrac><mo>)</mo><mo>&#x2212;</mo><mfrac><mrow><msub><mi>&#x3C4;</mi><mn>0</mn></msub></mrow><mrow><mn>2</mn><mi>&#x3BC;</mi></mrow></mfrac><mi>l</mi><mi>n</mi><mo>(</mo><mfrac><mrow><mi mathvariant="normal">&#x394;</mi><mi>T</mi></mrow><mrow><mn>2</mn><mi>&#x3C0;</mi><mi>h</mi><msub><mi>&#x3C4;</mi><mn>0</mn></msub><msubsup><mi>R</mi><mn>1</mn><mn>2</mn></msubsup></mrow></mfrac><mo>)</mo></mrow><annotation encoding="application/x-tex">\phi_{mod}=\frac{\Delta T}{4\pi h \mu}(\frac{1}{R_{1}^2}-\frac{2\pi h \tau_0}{\Delta T})-\frac{\tau_0}{2\mu}ln(\frac{\Delta T}{2\pi h \tau_0 R_1^2})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.8962079999999999em;"></span><span class="strut bottom" style="height:1.462648em;vertical-align:-0.56644em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">&#x3D5;</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">m</span><span class="mord mathit mtight">o</span><span class="mord mathit mtight">d</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">=</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.345em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">4</span><span class="mord mathit mtight" style="margin-right:0.03588em;">&#x3C0;</span><span class="mord mathit mtight">h</span><span class="mord mathit mtight">&#x3BC;</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.394em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathrm mtight">&#x394;</span><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mopen">(</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.37358em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist"><span style="top:0.27551428571428577em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.34480000000000005em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.394em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathrm mtight">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mbin">&#x2212;</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.345em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">&#x394;</span><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.4100999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight" style="margin-right:0.03588em;">&#x3C0;</span><span class="mord mathit mtight">h</span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.1132em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mclose">)</span><span class="mbin">&#x2212;</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.345em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">&#x3BC;</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.4100999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.1132em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="mord mathit">n</span><span class="mopen">(</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.37358em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight" style="margin-right:0.03588em;">&#x3C0;</span><span class="mord mathit mtight">h</span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.1132em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist"><span style="top:0.27551428571428577em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span style="top:-0.34480000000000005em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.394em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathrm mtight">&#x394;</span><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mclose">)</span></span></span></span></p>
<p>&#x7B49;&#x4EF7;&#x4E8E;</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>&#x3D5;</mi><mrow><mi>m</mi><mi>o</mi><mi>d</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">&#x394;</mi><mi>T</mi></mrow><mrow><mn>4</mn><mi>&#x3C0;</mi><mi>h</mi><mi>&#x3BC;</mi><msubsup><mi>R</mi><mn>1</mn><mn>2</mn></msubsup></mrow></mfrac><mo>&#x2212;</mo><mfrac><mrow><msub><mi>&#x3C4;</mi><mn>0</mn></msub></mrow><mrow><mn>2</mn><mi>&#x3BC;</mi></mrow></mfrac><mo>&#x2212;</mo><mfrac><mrow><msub><mi>&#x3C4;</mi><mn>0</mn></msub></mrow><mrow><mn>2</mn><mi>&#x3BC;</mi></mrow></mfrac><mi>l</mi><mi>n</mi><mo>(</mo><mfrac><mrow><mi mathvariant="normal">&#x394;</mi><mi>T</mi></mrow><mrow><mn>2</mn><mi>&#x3C0;</mi><mi>h</mi><msub><mi>&#x3C4;</mi><mn>0</mn></msub><msubsup><mi>R</mi><mn>1</mn><mn>2</mn></msubsup></mrow></mfrac><mo>)</mo></mrow><annotation encoding="application/x-tex">\phi_{mod}=\frac{\Delta T}{4\pi h \mu R_1^2}-\frac{\tau_0}{2\mu}-\frac{\tau_0}{2\mu}ln(\frac{\Delta T}{2\pi h \tau_0 R_1^2})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.872331em;"></span><span class="strut bottom" style="height:1.438771em;vertical-align:-0.56644em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">&#x3D5;</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">m</span><span class="mord mathit mtight">o</span><span class="mord mathit mtight">d</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">=</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.37358em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">4</span><span class="mord mathit mtight" style="margin-right:0.03588em;">&#x3C0;</span><span class="mord mathit mtight">h</span><span class="mord mathit mtight">&#x3BC;</span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist"><span style="top:0.27551428571428577em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span style="top:-0.34480000000000005em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.394em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathrm mtight">&#x394;</span><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mbin">&#x2212;</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.345em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">&#x3BC;</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.4100999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.1132em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mbin">&#x2212;</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.345em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">&#x3BC;</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.4100999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.1132em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="mord mathit">n</span><span class="mopen">(</span><span class="mord reset-textstyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.37358em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight" style="margin-right:0.03588em;">&#x3C0;</span><span class="mord mathit mtight">h</span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.1132em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist"><span style="top:0.27551428571428577em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span style="top:-0.34480000000000005em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.394em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathrm mtight">&#x394;</span><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mclose">)</span></span></span></span></p>
<p>tensorflow&#x5B9E;&#x73B0;&#x4EE3;&#x7801;&#x5982;&#x4E0B;&#xFF1A;</p>
<pre><code class="lang-python"><span class="hljs-keyword">import</span> tensorflow <span class="hljs-keyword">as</span> tf
<span class="hljs-keyword">import</span> numpy <span class="hljs-keyword">as</span> np
<span class="hljs-keyword">import</span> math

<span class="hljs-comment"># delta_T: T150-T50</span>
delta_t = np.array([<span class="hljs-number">4.398672</span>, <span class="hljs-number">3.816655</span>, <span class="hljs-number">3.619659</span>, <span class="hljs-number">3.22933</span>, <span class="hljs-number">2.923696</span>, <span class="hljs-number">2.889634</span>, <span class="hljs-number">2.670203</span>, <span class="hljs-number">2.466147</span>, <span class="hljs-number">2.287645</span>, <span class="hljs-number">2.011547</span>])
<span class="hljs-comment"># &#x8F6C;&#x901F;&#x6570;&#x636E;</span>
phi = np.array([<span class="hljs-number">0.6</span>, <span class="hljs-number">0.55</span>, <span class="hljs-number">0.5</span>, <span class="hljs-number">0.45</span>, <span class="hljs-number">0.4</span>, <span class="hljs-number">0.35</span>, <span class="hljs-number">0.3</span>, <span class="hljs-number">0.25</span>, <span class="hljs-number">0.2</span>, <span class="hljs-number">0.15</span>])

<span class="hljs-comment"># &#x5E38;&#x91CF;&#x6570;&#x636E;</span>
BATCH_SIZE = <span class="hljs-number">1</span>
h = <span class="hljs-number">0.1</span>
r1 = <span class="hljs-number">0.1</span>

<span class="hljs-comment"># &#x5B9A;&#x4E49;&#x8F93;&#x5165;&#x6570;&#x636E;</span>
x_data = delta_t.reshape(<span class="hljs-number">10</span>,<span class="hljs-number">1</span>)
y_data = phi.reshape(<span class="hljs-number">10</span>,<span class="hljs-number">1</span>)


<span class="hljs-comment"># &#x5B9A;&#x4E49;&#x53C2;&#x6570;</span>
mu = tf.Variable(tf.truncated_normal(shape=[<span class="hljs-number">1</span>, <span class="hljs-number">1</span>], mean=<span class="hljs-number">1</span>, stddev=<span class="hljs-number">0.5</span>))
tau = tf.Variable(tf.truncated_normal(shape=[<span class="hljs-number">1</span>, <span class="hljs-number">1</span>], mean=<span class="hljs-number">1</span>, stddev=<span class="hljs-number">0.5</span>))

<span class="hljs-comment"># &#x5B9A;&#x4E49;&#x5360;&#x4F4D;&#x7B26;</span>
x = tf.placeholder(tf.float32, [<span class="hljs-number">1</span>, <span class="hljs-number">1</span>])
y = tf.placeholder(tf.float32, [<span class="hljs-number">1</span>, <span class="hljs-number">1</span>])

<span class="hljs-comment"># &#x521B;&#x5EFA;&#x7684;&#x8BA1;&#x7B97;&#x7F51;&#x7EDC;</span>
prediction = x / (<span class="hljs-number">4</span>*math.pi*h*mu*(r1**<span class="hljs-number">2</span>)) - tau/(<span class="hljs-number">2</span>*mu) - tau/(<span class="hljs-number">2</span>*mu)*tf.log(x/(<span class="hljs-number">2</span>*math.pi*h*tau*(r1**<span class="hljs-number">2</span>)))

<span class="hljs-comment"># &#x5B9A;&#x4E49;&#x635F;&#x5931;&#x51FD;&#x6570;</span>
loss = tf.reduce_mean(tf.square(y-prediction))

<span class="hljs-comment"># &#x4F7F;&#x7528;&#x68AF;&#x5EA6;&#x4E0B;&#x964D;&#x6CD5;&#x8BAD;&#x7EC3;</span>
train_step = tf.train.GradientDescentOptimizer(<span class="hljs-number">0.01</span>).minimize(loss)

init_op = tf.global_variables_initializer()

<span class="hljs-keyword">with</span> tf.Session() <span class="hljs-keyword">as</span> sess:
    sess.run(init_op)
    <span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(<span class="hljs-number">100</span>):
        j = i % <span class="hljs-number">10</span>
        start = j
        end = j+<span class="hljs-number">1</span>
        _, predict_value, loss_value, mu_value, tau_value = sess.run([train_step,prediction,loss,mu,tau], feed_dict={x: x_data[start:end], y: y_data[start:end]})
        print(x_data[start:end])
        print(y_data[start:end])
        print(<span class="hljs-string">&quot;value = &quot;</span> + str(predict_value))
        print(<span class="hljs-string">&quot;loss = &quot;</span> + str(loss_value))
        print(<span class="hljs-string">&quot;mu = &quot;</span> + str(sess.run(mu)))
        print(<span class="hljs-string">&quot;tau = &quot;</span> + str(sess.run(tau)))
        print(<span class="hljs-string">&quot;=============================&quot;</span>)

    print(<span class="hljs-string">&quot;mu = &quot;</span> + str(sess.run(mu)))
    print(<span class="hljs-string">&quot;tau = &quot;</span> + str(sess.run(tau)))
</code></pre>
<p>&#x6BCF;&#x6B21;&#x8BAD;&#x7EC3;&#x7684;&#x6570;&#x636E;&#x90FD;&#x4E0D;&#x4E00;&#x81F4;&#xFF0C;&#x6682;&#x65F6;&#x5F97;&#x5230;&#x7ED3;&#x679C;&#x4E3A;</p>
<pre><code>mu = [[ 826.73492432]]
tau = [[ 12.30910397]]
</code></pre><p>&#x9A8C;&#x8BC1;&#x7A0B;&#x5E8F;</p>
<pre><code class="lang-python"><span class="hljs-keyword">import</span> math

x = [<span class="hljs-number">4.398672</span>, <span class="hljs-number">3.816655</span>, <span class="hljs-number">3.619659</span>, <span class="hljs-number">3.22933</span>, <span class="hljs-number">2.923696</span>, <span class="hljs-number">2.889634</span>, <span class="hljs-number">2.670203</span>, <span class="hljs-number">2.466147</span>, <span class="hljs-number">2.287645</span>, <span class="hljs-number">2.011547</span>]
expected = [<span class="hljs-number">0.6</span>, <span class="hljs-number">0.55</span>, <span class="hljs-number">0.5</span>, <span class="hljs-number">0.45</span>, <span class="hljs-number">0.4</span>, <span class="hljs-number">0.35</span>, <span class="hljs-number">0.3</span>, <span class="hljs-number">0.25</span>, <span class="hljs-number">0.2</span>, <span class="hljs-number">0.15</span>]
r1 = <span class="hljs-number">0.1</span>
h = <span class="hljs-number">0.1</span>

mu = <span class="hljs-number">826.73492432</span>
tau = <span class="hljs-number">12.30910397</span>

print(<span class="hljs-string">&quot;&#x5F53;mu=&quot;</span> + str(mu) + <span class="hljs-string">&quot;&#x4E14;tau=&quot;</span>+ str(tau)+<span class="hljs-string">&quot;&#x7684;&#x65F6;:&quot;</span>)
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(<span class="hljs-number">10</span>):
    y = (x[i]/(<span class="hljs-number">4</span>*math.pi*h*mu*(r1**<span class="hljs-number">2</span>))) - (tau/(<span class="hljs-number">2</span>*mu))*(<span class="hljs-number">1</span> + math.log(x[i]/(<span class="hljs-number">2</span>*math.pi*h*tau*(r1**<span class="hljs-number">2</span>))))
    print(<span class="hljs-string">&quot;mod = &quot;</span> + str(y) + <span class="hljs-string">&quot;, but mea = &quot;</span> + str(expected[i]))
</code></pre>
<p>&#x8F93;&#x51FA;&#x7684;&#x9A8C;&#x8BC1;&#x7ED3;&#x679C;:</p>
<pre><code>&#x5F53;mu=826.73492432&#x4E14;tau=12.30910397&#x7684;&#x65F6;:
mod = 0.3858686309147959, but mea = 0.6
mod = 0.3309030852908247, but mea = 0.55
mod = 0.31233572428304784, but mea = 0.5
mod = 0.27561400369308087, but mea = 0.45
mod = 0.2469353340965364, but mea = 0.4
mod = 0.24374393103120284, but mea = 0.35
mod = 0.22321049793670983, but mea = 0.3
mod = 0.20416087433744334, but mea = 0.25
mod = 0.18753847138982127, but mea = 0.2
mod = 0.1619201155386213, but mea = 0.15
</code></pre><footer class="page-footer"><span class="copyright">Copyright &#xA9; scottdu 2018 all right reserved&#xFF0C;powered by Gitbook</span><span class="footer-modification">&#x8BE5;&#x6587;&#x4EF6;&#x4FEE;&#x8BA2;&#x65F6;&#x95F4;&#xFF1A;
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